Introduction To Numerical Methods For Variational Problems

21 Hans Petter Langtangen Kent-Andre Mardal Introduction to Numerical Methods for Variational Problems Editorial Board T. J.Barth M.Griebel D.E.Keyes R.M.Nieminen D.Roose T.Schlick Texts in Computational Science and Engineering Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick 21 More information about this series at http://www.springer.com/series/5151 Hans Petter Langtangen • Kent-Andre Mardal Introduction to Numerical Methods for Variational Problems 123 Hans Petter Langtangen (deceased) BioComp Simula Research Laboratory Lysaker, Norway Kent-Andre Mardal Department of Mathematics University of Oslo Oslo, Norway ISSN 1611-0994 ISSN 2197-179X (electronic) Texts in Computational Science and Engineering ISBN 978-3-030-23787-5 ISBN 978-3-030-23788-2 (eBook) https://doi.org/10.1007/978-3-030-23788-2 Mathematics Subject Classification (2010): 65K05, 74S05, 68N01, 35R10 © Springer Nature Switzerland AG 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland This easy-to-read book introduces the basic ideas and technicalities of least squares, Galerkin, and weighted residual methods for solving partial differential equations. Special emphasis is put on finite element methods. Preface The present book is essentially a book on the finite element method, although we discuss many other choices of basis functions and other applications than partial differential equations. The literature on finite elements contains books of many different flavors, ranging from an abstract view of the method [5, 6, 9, 13, 26] to a more practical, algorithmic treatment of the subject [18, 33]. The present book has a very strong algorithmic focus (“how to compute”), but formulate the method in abstract form with variational forms and function spaces. One highl